|
Abbe Error
Abbe error, named after Ernst Abbe, also called sine error, describes the magnification of angular error over distance. For example, when one measures a point that is 1 meter away at 45 degrees, an angular error of 1 degree corresponds to a positional error of over 1.745 cm, equivalent to a distance-measurement error of 1.745%. In machine design, some components are particularly sensitive to angular errors. For example, slight deviations from parallelism of the spindle axis of a lathe to the tool motion along the bed of the machine can lead to relatively large (undesired) taper along the part (i.e a non-cylindrical part). Vernier calipers are not free from abbe error, while screw gauges are free from abbe error. Abbe error is the product of the abbe offset and the sine of angular error in the system. Abbe error can be detrimental to dead reckoning In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Abbe
Ernst Karl Abbe HonFRMS (23 January 1840 – 14 January 1905) was a German physicist, optical scientist, entrepreneur, and social reformer. Together with Otto Schott and Carl Zeiss, he developed numerous optical instruments. He was also a co-owner of Carl Zeiss AG, a German manufacturer of scientific microscopes, astronomical telescopes, planetariums, and other advanced optical systems. Personal life Abbe was born 23 January 1840 in Eisenach, Saxe-Weimar-Eisenach, to Georg Adam Abbe and Elisabeth Christina Barchfeldt. He came from a humble home – his father was a foreman in a spinnery. Supported by his father's employer, Abbe was able to attend secondary school and to obtain the general qualification for university entrance with fairly good grades, at the Eisenach Gymnasium, which he graduated from in 1857. By the time he left school, his scientific talent and his strong will had already become obvious. Thus, in spite of the family's strained financial situation, his fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abbe Sine Condition
The Abbe sine condition is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It was formulated by Ernst Abbe in the context of microscopes. The Abbe sine condition says that the sine of the object-space angle \alpha_o should be proportional to the sine of the image space angle \alpha_i Furthermore, the ratio equals the magnification of the system. In mathematical terms this is: :\frac = \frac = , M, where the variables (\alpha_o, \beta_o) are the angles (relative to the optic axis) of any two rays as they leave the object, and (\alpha_i, \beta_i) are the angles of the same rays where they reach the image plane (say, the film plane of a camera). For example, (\alpha_o, \alpha_i) might represent a paraxial ray (i.e., a ray nearly parallel with the optic axis), and (\beta_o, \beta_i) might represent a marginal ray (i.e., a ray with the largest angle admitted by the system apert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lathe
A lathe () is a machine tool that rotates a workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, and turning, with tools that are applied to the workpiece to create an object with symmetry about that axis. Lathes are used in woodturning, metalworking, metal spinning, thermal spraying, parts reclamation, and glass-working. Lathes can be used to shape pottery, the best-known design being the Potter's wheel. Most suitably equipped metalworking lathes can also be used to produce most solids of revolution, plane surfaces and screw threads or helices. Ornamental lathes can produce three-dimensional solids of incredible complexity. The workpiece is usually held in place by either one or two ''centers'', at least one of which can typically be moved horizontally to accommodate varying workpiece lengths. Other work-holding methods include clamping the work about the axis of rotation using a chuc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dead Reckoning
In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously determined position, or fix, and then incorporating estimates of speed, heading direction, and course over elapsed time. The corresponding term in biology, used to describe the processes by which animals update their estimates of position or heading, is path integration. Dead reckoning is subject to cumulative errors. Advances in navigational aids that give accurate information on position, in particular satellite navigation using the Global Positioning System, have made simple dead reckoning by humans obsolete for most purposes. However, inertial navigation systems, which provide very accurate directional information, use dead reckoning and are very widely applied. Etymology The term "dead reckoning" was not originally used to abbreviate "deduced reckoning," nor is it a misspelling of the term "ded reckoning." The use of "ded" or "deduced reckoning" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error
An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistics, "error" refers to the difference between the value which has been computed and the correct value. An error could result in failure or in a deviation from the intended performance or behavior. Human behavior One reference differentiates between "error" and "mistake" as follows: In human behavior the norms or expectations for behavior or its consequences can be derived from the intention of the actor or from the expectations of other individuals or from a social grouping or from social norms. (See deviance.) Gaffes and faux pas can be labels for certain instances of this kind of error. More serious departures from social norms carry labels such as misbehavior and labels from the legal system, such as misdemeanor and crime. Departures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities. These trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation. History Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They, and later the Babylonians, studied the ratios of the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
